1995 Jeep Laredo Brakes Slow. But fail on stop.

The brakes work fine and have good pressure when initially pressed, slowing the vehicle appropriately. As the vehicle approaches the point of stopping, the break pressure begins to give away, almost skipping and jerking. The vehicle moves forward like the brake has been released. Increased pressure on the pedal then stops the vehicle. But the pedal is now very spongy allowing me to press it a further four or five inches up and down with an obvious pressure release sound eminating from the pedal area - all while the vehicle is stopped. When the pedal is fully released the vehicle moves forward normally. During normal drive the brakes work fine. Only when coming to a stop does the above happen.
As a side note, the vehicle does not have a working emergency brake system, it having been removed. My assumption was that this problem had something to do with that, but I would like your advice. Thank you.